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arXiv · 2005.12353

Non-Archimedean entire curves in projective varieties dominating an elliptic curve

Jackson S. Morrow
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Abstract

Let $K$ be an algebraically closed, complete, non-Archimedean valued field of characteristic zero. We prove the non-Archimedean Green--Griffiths--Lang conjecture for projective surfaces of irregularity one. More precisely, we prove that if $X/K$ is a groupless, projective surface that admits a dominant morphism an elliptic curve, then $X$ is $K$-analytically Brody hyperbolic. The main ingredient in our proof is a theorem concerning the algebraic degeneracy of non-Archimedean entire curves in projective, pseudo-groupless varieties admitting a dominant morphism to an elliptic curve.

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Jackson S. Morrow. 2020-05-25. Non-Archimedean entire curves in projective varieties dominating an elliptic curve. https://arxiv.org/abs/2005.12353

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